Effect of bio-polymer viscosity on residual oil saturation in carbonate reservoirs

ABSTRACT

Polymer flooding models for carbonate reservoirs and related methods include the trapping number effect on residual oil saturation. A method for predicting oil recovery from a reservoir using enhanced oil recovery techniques can include simulating the reservoir in a computer simulation (202). Injection of a fluid (204) can be simulated in the computer simulation and an enhanced oil recovery technique can be simulated to simulate the oil recovery from die reservoir (206).

CROSS-REFERENCE

This application claims the benefit of and priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application Ser. No. 62/898,789 filed Sep. 11, 2019, which is incorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

Oil can be recovered from a reservoir using primary and secondary recovery mechanisms. However, even after these mechanisms have been employed, up to 60% of original oil-in-place (OOIP) can remain in the reservoir. Enhanced oil recovery (EOR) techniques can be used to recover some of the remaining oil, however, the composition of some reservoirs can reduce the efficiency of even the most effective EOR technique, for example, polymer flooding. For example, hydrocarbon reservoirs that can be characterized with carbonate lithology, high temperature, high salinity, high heterogeneity with low permeability, and mixed-to-oil wettability can results in low oil recovery when polymer flooding EOR techniques are used. Models can be used to simulate the oil recovery using polymer flooding techniques, however, these models may not accurately predict the performance of the polymer flooding behavior in reservoirs with certain compositions, for example, carbonate reservoirs. It may be desirable to have a model that more accurately simulates oil recovery using polymer flooding techniques in carbonate reservoirs.

BRIEF SUMMARY

The following presents a simplified summary of embodiments of the invention in order to provide a basic understanding of the invention. This summary is not an extensive overview of the invention. It is not intended to identify key/critical elements of the invention nor to delineate the scope of the invention. Its sole purpose is to present some embodiments of the invention in a simplified form as a prelude to the more detailed description that is presented later.

Embodiments described herein are directed to a method of generating a prediction of an oil recovery from a reservoir induced by accomplishing an enhanced oil recovery technique that comprises injection of one or more fluids into the reservoir. The method can include simulating the reservoir in a computer simulation, simulating injection of a first fluid into the reservoir in the computer simulation, and simulating the oil recovery from the reservoir induced by accomplishing an enhanced oil recovery technique in the computer simulation so as to account for an estimated change in aqueous viscosity that would be induced by injection of the first fluid into the reservoir.

In some embodiments of the method, the reservoir can be simulated having various properties. For example, the method can include the computer simulation simulating the reservoir in three dimensions and multiphase flow within the reservoir.

In some embodiments of the method, the first fluid can include various types of fluid. For example, the first fluid can include a polymer.

In some embodiments of the method, the method includes simulating injection of a second fluid into the reservoir in the computer simulation. In some embodiments of the method, the first fluid is injection into the reservoir after the second fluid is injected into the reservoir in the enhanced oil recovery technique. In some embodiments of the method, the second fluid includes water.

In some embodiments of the method, the method includes calculating a trapping number (N_(Tl)) for the reservoir that accounts for the first fluid within the reservoir, wherein the trapping number is defined as:

$\frac{v\mu}{\sigma_{ow}}$

where ν is a Darcy velocity of a core sample comprising the same or similar material as the reservoir, μ is an aqueous phase viscosity, and σ_(ow) is an interfacial tension between oil and water.

In another aspect, a method includes generating a model of a hydrocarbon reservoir having parameters, determining a critical trapping number for the hydrocarbon reservoir based in part on a substrate of the hydrocarbon reservoir, determining a trapping number of the substrate for a given injection volume, determining whether the trapping number has exceeded the critical trapping number, and modifying, based in part on the determination that the critical trapping number has been exceeded, one or more parameters of the model of the hydrocarbon reservoir.

In some embodiments of the method, generating the model of the hydrocarbon reservoir includes generating the hydrocarbon reservoir. For example, the hydrocarbon reservoir can be generated in three dimensions and modeling multiphase flow within the hydrocarbon reservoir.

In some embodiments of the method, hydrocarbon reservoir can include adjustable parameters. For example, the parameters of the hydrocarbon reservoir can include residual oil and relative permeability. In some embodiments of the method, modifying one or more parameters of the model comprises modifying the residual oil and relative permeability parameters.

In some embodiments of the method, determining a trapping number of the substrate for a given injection volume includes simulating injection of a first fluid into the model of the hydrocarbon reservoir. In some embodiments of the method, the first fluid includes a polymer.

In some embodiments of the method, the method further includes determining expected oil recovery for a reservoir having a substrate that is the same as or similar to the substrate of the model of the hydrocarbon reservoir. In some embodiments of the method, determining the expected oil recovery includes determining the expected oil recovery using an enhanced oil recovery technique.

In another aspect, a method of simulating oil recovery from a biopolymer injection cycle in a hydrocarbon carbonate reservoir includes: determining a critical trapping number representative of a simulated hydrocarbon carbonate reservoir based in part on a composition of a reservoir substrate; determining whether, for a given injection volume, a trapping number of a substrate of the hydrocarbon carbonate reservoir has exceeded a critical trapping number; and modifying the residual oil and relative permeability parameters of the simulated hydrocarbon carbonate reservoir based on the determination that the critical trapping number has been exceeded.

In some embodiments of the method, the method further comprises simulating the hydrocarbon carbonate reservoir. For example, the hydrocarbon reservoir can be simulated prior to determining the critical trapping number.

In some embodiments of the method, the hydrocarbon carbonate reservoir is simulated in three dimensions. The hydrocarbon carbonate reservoir can include multiphase flow within the hydrocarbon carbonate reservoir.

In some embodiments of the method, prior to determining whether the trapping number of the substrate has exceeded the critical trapping number, the method further comprises determining the trapping number of the substrate for the given injection volume. In some embodiments of the method, the trapping number (N_(Tl)) is define as

$\frac{v\mu}{\sigma_{ow}}$

where ν is a Darcy velocity of a core sample comprising the same or similar material as the hydrocarbon carbonate reservoir, μ is an aqueous phase viscosity, and σ_(ow) is an interfacial tension between oil and water. In some embodiments of the method, determining the trapping number comprises simulating injection of a first fluid into the simulated hydrocarbon carbonate reservoir. In some embodiments of the method, the first fluid comprises a polymer.

In some embodiments of the method, the method further includes determining expected oil recovery for a reservoir having a substrate that is the same as or similar to the substrate of the simulated hydrocarbon carbonate reservoir. In some embodiments of the method, determining the expected oil recovery includes determining the expected oil recovery using an enhanced oil recovery technique.

In another aspect a computer system includes a processor and reconfigurable memory. The processor and reconfigurable memory operable to: determine a critical trapping number representative of a simulated hydrocarbon reservoir based in part on a composition of a reservoir substrate; determine whether, for a given injection volume, a trapping number of the substrate has exceeded the critical trapping number; and modify residual oil and relative permeability parameters of the simulated hydrocarbon reservoir based on the determination that the critical trapping number has been exceeded.

In some embodiments of the computer system, prior to determining the critical trapping number, the processor and reconfigurable memory are further operable to simulate the hydrocarbon reservoir. In some embodiments of the computer system, the hydrocarbon reservoir is simulated in three dimensions and includes multiphase flow within the hydrocarbon reservoir.

In some embodiments of the computer system, prior to determining whether the trapping number of the substrate has exceeded the critical trapping number, the method further comprises determining the trapping number of the substrate for the given injection volume. In some embodiments of the computer system, the trapping number (N_(Tl)) is defined as

$\frac{v\mu}{\sigma_{ow}},$

where ν is a Darcy velocity or a core sample comprising the same or similar material as the reservoir, μ is an aqueous phase viscosity, and σ_(ow) is an interfacial tension between oil and water.

In some embodiments of the computer system, the processor and reconfigurable memory are further operable to, determine expected oil recovery for a reservoir having a substrate that is the same as or similar to the substrate of the simulated hydrocarbon reservoir. In some embodiments of the computer system, the expected oil recovery is determined for oil recovery using an enhanced oil recovery technique.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments in accordance with the present disclosure will be described with reference to the drawings, in which:

FIG. 1 illustrates an example computer system for generating and modifying a hydrocarbon reservoir model;

FIG. 2 is a flowchart illustrating a process for modifying a simulated hydrocarbon reservoir for use with the computer system of FIG. 1;

FIG. 3 is a flowchart illustrating a process for modifying a simulated hydrocarbon reservoir for use with the computer system of FIG. 1;

FIG. 4 is an example simulated hydrocarbon reservoir for use with the computer system of FIG. 1;

FIG. 5 is a graph showing history matched cumulative oil recovery for waterflooding followed by polymer flooding cycles;

FIG. 6 is a graph showing the effect of inaccessible pore volume (IPV) on tertiary oil recovery by polymer flooding;

FIG. 7 is a graph showing the effect of polymer adsorption on tertiary oil recovery by polymer flooding;

FIG. 8 is a graph showing the effect of permeability reduction on tertiary oil recovery by polymer flooding;

FIG. 9 is a graph showing the effect of shear rate coefficient on tertiary oil recovery by polymer flooding;

FIG. 10 is a graph showing the effect of makeup water hardness on tertiary oil recovery by polymer flooding;

FIG. 11 is a graph showing the remaining oil saturation as a function of capillary number;

FIG. 12 is a graph showing a modeled capillary desaturation curve (CDC) for both sandstone and carbonate rocks;

FIG. 13 is a graph showing relative permeability curves before and after exceeding the critical trapping number;

FIG. 14 is a graph showing the effect of trapping number on tertiary oil recovery by polymer flooding; and

FIG. 15 is a graph showing history matched cumulative oil recovery for waterflooding followed by polymer flooding cycles.

DETAILED DESCRIPTION

In the following description, various embodiments will be described. For purposes of explanation, specific configurations and details are set forth in order to provide a thorough understanding of the embodiments. However, it will also be apparent to one skilled in the art that the embodiments may be practiced without the specific details. Furthermore, well-known features may be omitted or simplified in order not to obscure the embodiment being described.

Oil recovery techniques can be used to extract oil from oil reservoirs. However, primary and secondary oil recovery methods can still leave a large amount of oil remaining in a reservoir. For example, up to 60% of original oil-in-place (OOIP) can remain in a reservoir. Tertiary recovery techniques (e.g., enhanced oil recovery (EOR)) can be used to extract some of the OOIP, for example, by targeting unswept oil and/or capillary trapped oil saturations. EOR techniques can be or include solvent, thermal, chemical, and/or any suitable technique.

Polymer flooding is an EOR technique that can increase oil sweep efficiency, for example, by targeting by-passed oil and/or recover residual capillary-trapped oil. Polymer flooding is often used in sandstone reservoirs that can have properties including temperatures below 60° C., low formation salinity (<100 g/L), and/or moderate to high permeability (>40 mD). However, certain reservoirs can have properties that reduce the effectiveness of polymer flooding. For example, hydrocarbon reservoirs can have properties including carbonate lithology, high temperature, high salinity, high heterogeneity with low permeability, and mixed-to-oil wettability.

Various techniques have been investigated for improving oil recovery in carbonate reservoirs using polymer flooding, for example, discovery/synthesizing new polymers that can withstand the reservoir conditions and/or combining polymer flooding with other EOR techniques to expand its application envelope. However, due to the challenging conditions of carbonate reservoirs, these techniques have mainly been investigated in lab settings. Modeling of polymer behavior in carbonate reservoirs can be used improve the efficiency of polymer flooding in real world situations.

Traditionally, polymer flooding models for sandstone reservoirs may not include the trapping number effect on residual oil saturation. However, for polymer flooding models for carbonate reservoirs, modeling the trapping number effect on residual oil can increase the accuracy of the model. Using a computer system, a polymer flooding model that includes the trapping number effect on residual oil saturation can be developed. Using the computer system, the polymer flooding model can be validated, for example, by history matching biopolymer corefloods with the model.

Turning to FIG. 1, an example computer system 100 for generating and modifying a hydrocarbon reservoir model is shown. As shown, the example embodiment includes a model generating module 102, a determining module 104, a comparing module 106 and a model modifying module 108. Computer system 100 may represent a single component, multiple components located at a central location, or multiple components distributed throughout multiple locations. For example, computer system 100 may represent components of interconnected computer systems that are capable of communicating information between one another. In general, computer system 100 may include any appropriate combination of hardware and/or software suitable to provide the described functionality.

Processor 110 is operable to execute instructions associated with the functionality provided by computer system 100. Processor 110 may comprise one or more general purpose computers, dedicated microprocessors, or other processing devices capable of communicating electronic information. Examples of processor 110 include one or more application-specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), digital signal processors (DSPs) and any other suitable specific or general purpose processors.

Memory 112 stores processor instructions, inventory requests, reservation information, state information for the various components of inventory sorting system 100 and/or any other appropriate values, parameters, or information utilized by computer system 100 during operation. Memory 112 may represent any collection and arrangement of volatile or nonvolatile, local or remote devices suitable for storing data. Examples of memory 112 include, but are not limited to, random access memory (RAM) devices, read only memory (ROM) devices, magnetic storage devices, optical storage devices or any other suitable data storage devices.

The model generating module 102 can generate a 3D model of an oil reservoir based on data collected during oil recovery techniques. The model can be used to simulate the process of removing the oil from the oil reservoir using primary, secondary, and/or EOR techniques. For example, the model can be used to simulate waterflooding and/or polymer flooding of an oil reservoir. The model may also be used to predict the amount of oil recovery using secondary and/or EOR techniques. In various embodiments, the model can be or include a 3D multiphase-flow, transport, and chemical-flooding simulator and/or a carbonate core model.

Determining module 104 can determine one or more parameters for the reservoir model generated by model generating module 102. In various embodiments, the determining module 104 can determine a critical trapping number based on material properties of the modeled reservoir. For example, a critical trapping number can be determined for a carbonate reservoir model and/or a sandstone reservoir model. In further embodiments, the determining module 104 can determine a trapping number for a given injection volume of polymer.

Comparing module 106 can compare the critical trapping number with the determined trapping number. For example, the comparing module 106 can compare the critical trapping number with the determined trapping number to determine whether the critical trapping number has been exceed. Based on the comparing, one or more parameters of the model can be adjusted to more accurately reflect the real world behavior of the reservoir.

The modifying module 108 can modify one or more parameters of the model based on the comparing of the critical trapping number with the determined trapping number. For example, if the comparing module 106 determines the trapping number has exceeded the critical trapping number, the residual oil and relative permeability parameters of the model can be modified to more accurately reflect the real world behavior of the reservoir. The modifying of the model can be used to increase the accuracy of the model.

In various embodiments, the computer system 100 can include a communication interface module 114 that facilitates communication between modules and/or components of the computer system 100. Depending on the configuration of computer system 100, communication interface module 114 may be responsible for facilitating either or both of wired and wireless communication between the modules and/or components of the computer system 100. In particular embodiments, the computer system 100 may communicate using communication protocols such as 802.11, Bluetooth, or Infrared Data Association (IrDA) standards.

In general, generating module 102, determining module 104, comparing module 106, modifying module 108, and/or communication interface module 114 may each represent any appropriate hardware and/or software suitable to provide the described functionality. In addition, as noted above, computer system 100 may, in particular embodiments, represent multiple different discrete components and any or all of resource generating module 102, determining module 104, comparing module 106, modifying module 108, and/or communication interface module 114 may represent components physically separate from the remaining elements of computer system 100. Moreover, any two or more of generating module 102, determining module 104, comparing module 106, modifying module 108, and/or communication interface module 114 may share common components. For example, in particular embodiments, generating module 102, determining module 104, comparing module 106, and/or modifying module 108 represent computer processes executing on processor 110 and communication interface module 114 comprises a wireless transmitter, a wireless receiver, and a related computer process executing on processor 110.

Turning to FIG. 2, a flowchart illustrating a process for modifying a simulated hydrocarbon reservoir for use with the computer system of FIG. 1 is shown. The process 200 at block 202 can include simulating a reservoir in a computer simulation. For example, the simulated reservoir can be the same as or similar to the carbonate core model 400 shown in FIG. 4. In various embodiments, the computer simulation can be generating using computer system 100. The hydrocarbon reservoir can be simulated in three dimension and/or with multiphase flow within the reservoir.

The process 200 at block 204 can include simulating injection of a first fluid into the reservoir in the computer simulation. In various embodiments, the first fluid simulation can be or include a polymer. In some embodiments, a second fluid simulation (e.g., water) can be injected into the reservoir in the computer simulation. In further embodiments, the second fluid can be injected into the reservoir prior to the first fluid being injected into the reservoir. However, the first fluid can be injected into the reservoir prior to the second fluid being injection into the reservoir.

The process 200 at block 206 can include simulating oil recovery from the reservoir induced by accomplishing an enhanced oil recovery technique in the computer simulation, for example, to account for an estimated change in aqueous viscosity that would be induced by injection of the first fluid into the reservoir. In various embodiments, the enhanced oil recovery technique can be or include polymer flooding. In further embodiments, the process 200 at block 206 can include calculating a trapping number for the reservoir that accounts for the first fluid within the reservoir. The trapping number can be calculated, for example, using

$N_{Tl} = {N_{cl} = \frac{v\mu}{\sigma_{ow}}}$

where ν is Darcy velocity in the core, μ is the aqueous phase viscosity, and σ_(ow) is the interfacial tension between oil and water.

Turning to FIG. 3, another flowchart illustrating a process 300 for generating and modifying a hydrocarbon reservoir model for use with the computer system 100 of FIG. 1 is shown. The process 300 at block 302 can include generating a hydrocarbon reservoir model, for example, the carbonate core model 400 shown in FIG. 4. The reservoir model can be generated using model generating module 102. In various embodiments, the hydrocarbon reservoir model can include various adjustable parameters to more accurately model the effect of oil recovery techniques on the reservoir. For example, the sensitivity of various input parameters, the inaccessibility of pore volumes, polymer absorption, permeability reduction, equivalent shear rate, the hardness of makeup water, and/or the trapping number can be adjusted to better match the performance of the model reservoir with historical data of how a real world reservoir would function. In further embodiments, generating a model that includes the effect of the trapping number on residual oil saturation can result in a model that more accurately predicts the polymer flooding effect on oil recovery.

The process 300 at block 304 can include determining a critical trapping number for the model (e.g., a critical capillary number). For example, a critical trapping number can be determined based at least in part on a composition of a substrate of the reservoir. In various embodiments, the a critical trapping number can be determined for a sandstone reservoir and/or for a carbonate reservoir. The critical trapping number can be determined based on the properties of the reservoir and/or can be determined based on the capillary desaturation curve (CDC). For example, the critical trapping number of a sandstone reservoir can be determined to be about 10⁻⁶ and the critical trapping number for carbonates can be lower than the critical trapping number of sandstone (e.g., about 10⁻⁸). The critical trapping number for carbonate can be more difficult to determine because the carbonate rocks that make up the carbonate reservoir are heterogeneous. The CDC be determined based on measurements made in a lab. For example, the true residual oil, initial plateau of the CDC can be determined. The injection rate, viscosity of fluid, and/or a decrease of interfacial tension (IFT) can then be adjusted and the shape of further residual oil saturation reduction with increasing trapping number can be determined.

The process 300 at block 306 can include determining whether a trapping number for a given injection volume has exceeded the critical trapping number. For example, a trapping number (N_(Tl)), for a given injection volume can be determined using the equation

$N_{Tl} = {\frac{❘{\overset{\overset{\rightarrow}{\rightarrow}}{k}.\left\lbrack {{\nabla\Phi_{l^{\prime}}} + {{g\left( {\rho_{l^{\prime}} - \rho_{l}} \right)}{\nabla D}}} \right\rbrack}❘}{\sigma_{{ll}^{\prime}}}.}$

However, in various embodiments the trapping number can be determine using the capillary number and bond number. Equations

${N_{Tl} = \sqrt{N_{cl}^{2} + {2N_{cl}N_{Bl}\sin\theta} + N_{Bl}^{2}}},{N_{cl} = \frac{❘{\overset{\overset{\rightarrow}{\rightarrow}}{k}.\left\lbrack {\nabla\Phi_{l^{\prime}}} \right.}❘}{\sigma_{{ll}^{\prime}}\cos\theta}},{N_{Bl} = \frac{{kg}\left( {\rho_{l^{\prime}} - \rho_{l}} \right)}{\sigma_{{ll}^{\prime}}\cos\theta}},$

and ∇Φ_(1{circumflex over ( )}′)=∇P_(1{circumflex over ( )}′)−gρ_(1{circumflex over ( )}′) VD can be used to determine the trapping number, where l′ is the displacing phase (aqueous phase including polymer), l is the displaced phase (oil phase), ∇Φ_(l′) is the flow potential gradient of the displacing phase, k is the permeability, g is the gravitational force constant, θ is the angle measured from the horizontal level or the contact angle, and σ_(ll′) is the interfacial tension between the displacing and displaced phases.

The determined trapping number can be compared with the critical trapping number to determine whether the trapping number has exceeded the critical trapping number. The process 300 at block 308 can include modifying parameters of the hydrocarbon reservoir model. For example, if the trapping number exceeds the critical trapping number the residual oil and/or relative permeability parameters of the model can be modified. Modifying the parameters can improve the accuracy of the model, for example, by more accurately predicting the amount of OOIP that can be recovered during polymer flooding. Increasing the accuracy of the model can additionally or alternatively allow the model to more closely match data collected using scientific or real world techniques.

A person of ordinary skill in the art will appreciate the various embodiments described above may be used with any number of suitable examples. However, described herein is a specific example which may be used with the embodiments described herein to generate and modify a model of a carbonate reservoir. For example, a significant fraction of oil remains in the reservoir after both primary and secondary recovery mechanisms, which is roughly approximated as 60% original oil-in-place (OOIP). The latter raised the interest in tertiary recovery methods, also known as enhanced oil recovery (EOR) methods. Different EOR methods are used including solvent, thermal, chemical and others. These methods usually target both unswept oil as well as capillary trapped oil saturations (Lake, L. W., 1989. Enhanced Oil Recovery. Englewood Cliffs, N. J., Prentice Hall, hereinafter, “Lake, 1989”).

Polymer flooding is a process that can include a water-soluble chemical (polymer) being dissolved into water to increase the injected water viscosity. Additionally and/or alternatively, the water mobility may be reduced and/or the oil sweep efficiency may increase. Polymer flooding is a well-established enhanced oil recovery (EOR) technique that increases oil sweep efficiency by targeting by-passed oil and/or recover residual capillary-trapped oil. Standnes, D. C. and Skjevrak, I., 2014. Literature Review of Implemented Polymer Field Projects. Journal of Petroleum Science and Engineering, 122: 761-775, hereinafter, “Standnes and Skjevrak (2014)” reported over 40 successful polymer flooding projects worldwide, most of them in the United States, Canada, and China. Some of these projects date back as early as 1964. The overwhelming majority of these applications are in sandstone reservoirs in temperatures well below 60° C., low formation salinity (<100 g/L), and moderate to high permeability (>40 mD). In the Middle East, hydrocarbon reservoirs are often characterized with carbonate lithology, high temperature, high salinity, and high heterogeneity with low permeability, and mixed-to-oil wettability. The combined effects of these conditions results in low oil recovery and in hampering the application of the most effective EOR technique.

As a result, researchers have been working toward extending polymer flooding success to carbonate reservoirs in the aforementioned challenging reservoir conditions. These efforts are usually focused on discovering/synthesizing new polymers that are able to withstand the harsh reservoir conditions. Others propose combining polymer flooding with other EOR techniques to expand its application envelope (Vermolen, E., Van Haasterecht, M. J., Masalmeh, S. K., Faher, M. J., Boersma, D. M., and Gruenenfelder, M. A., 2011. Pushing the Envelope for Polymer Flooding Towards High-Temperature and High-Salinity Reservoirs with Polyacrylamide Based Ter-Polymers. Paper SPE 141497, SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, hereinafter, “Vermolen et al., 2011”; Al-Shalabi, E. W. and Sepehrnoori, K., 2017. Low Salinity and Engineered Water Injection for Sandstone and Carbonate Reservoirs. Gulf Professional Publishing, Elsevier, 1^(st) Edition, pp. 178, ISBN: 978-0-12-813604-1, Cambridge, USA, hereinafter, “Al-Shalabi and Sepehrnoori 2017”). Due to the challenging conditions of carbonates, the main focus of the work has been concentrated in the laboratory with very few works been reported about modeling of the polymer behavior in these reservoirs.

The invention described in this work highlights the common practice of neglecting trapping number effect on residual oil saturation during modeling polymer flooding behavior in sandstones. This invention shows that this is not the case for carbonates where modeling trapping number effect on residual oil saturation is needed for better modeling of polymer flooding effect on oil recovery. This observation was supported by history matching an experimental coreflood for a biopolymer effect on oil recovery in carbonates. Conventional models for polymer performance in sandstone were applied and a good match was not possible unless the effect of trapping number was introduced. A detailed description of the case is provided below.

The work described here is a continuation of already published work by Al-Shalabi, E. W., 2018. Numerical Modeling of Biopolymer Flooding in High-Temperature high-Salinity Carbonate Cores. Paper SPE 28447, SPE Offshore Technology Conference-Asia, Kuala Lumpur, Malaysia, hereinafter, “Al-Shalabi (2018)”. In the previous work, a carbonate core model, as shown in FIG. 5, was used to history match a waterflooding process on a Middle Eastern carbonate core. Later, the model was utilized to make predictions of oil recovery by Schizophyllan biopolymer in both secondary and tertiary modes of injection. Quadri, S. M. R., 2015. Identification and Evaluation of Polymers for EOR in High Temperature, High Salinity Carbonate Reservoir Conditions. Master Thesis, Khalifa University of Science and Technology, Abu Dhabi, UAE, hereinafter, “Quadri (2015)” reported the biopolymer properties from the screening studies conducted. Also, the UTCHEM simulator was used to predict the effect of biopolymer on oil recovery from carbonates. This simulator is 3D multiphase-flow, transport, and chemical-flooding simulator developed at the University of Texas at Austin (UTCHEM—9.0 Technical Documentation, 2000. The University of Texas at Austin, Volume II, Texas, USA, hereinafter, “Technical Documentation, 2000”). This work describes the validation of the previous biopolymer predictions through history matching the biopolymer corefloods conducted by Li, J., 2015. Experimental Investigation and Simulation of Polymer Flooding in High Temperature high Salinity Carbonate Reservoirs. Master Thesis, Khalifa University of Science and Technology, Abu Dhabi, UAE, hereinafter, “Li (2015)”. A brief description of experimental data is presented in the section below.

Experimental Data

Quadri (2015) presented a screening study for Schizophyllan biopolymer to be used in Middle Eastern carbonate reservoirs with high temperature and high salinity conditions. The latter polymer showed shear thinning behavior with excellent thermal stability (at 120° C.) and salt tolerance (up to 200,000 ppm). In addition, Schizophyllan showed good injectivity on cores with permeability higher than 30 mD. Dynamic adsorption was also discussed on cores of different permeabilities (3-163 mD) and was found to be low within 7-48 μg/g of rock. Later, Li (2015) conducted several corefloods to highlight the effect of Schizophyllan biopolymer on oil recovery where additional oil recovery was between 7-10% post waterflooding. A coreflood can include a process in which a core (e.g., rock) is included in a displacement experiment. A displacement experiment can include saturating the core with a first fluid (e.g., oil) and displacing the core using a second fluid (e.g., water and/or water combined with polymer). Moreover, a polymer concentration of 200 ppm was used to enhance oil recovery from these cores. The current study utilizes polymer solution properties through the screening studies conducted by Quadri (2015) as well as rock and fluid properties through corefloods conducted by Li (2015).

One of the corefloods conducted by Li (2015) was utilized to validate the previous predictions (Al-Shalabi, 2018). The selected coreflood includes a secondary formation waterflooding followed by a tertiary biopolymer flooding. In this coreflood, the core was saturated with dead reservoir oil at irreducible water saturation, and then, formation water was injected at reservoir conditions (248° F. and 3000 psig). Afterwards, polymer flooding was used to further enhance oil recovery from that core. The core plug used has an average porosity of 13.12% and an average liquid permeability of 30.5 mD. More information about the screening work of the biopolymer used and the coreflood conducted can be found elsewhere (Quadri, 2015; Li, 2015). It is worth mentioning that the secondary formation water cycle was history matched in Al-Shalabi's (2018) previous work, as shown in FIG. 5, where cumulative oil recovery is shown on the y-axis and cumulative injection is shown on the x-axis. However, this study is mainly focused on history matching the tertiary biopolymer injection cycle.

Biopolymer Validation Study (Tertiary Injection)

As was previously mentioned, Li (2015) conducted several corefloods to highlight the effect of Schizophyllan biopolymer on oil recovery where additional oil recovery was between 7-10% OOIP post waterflooding. In their coreflood, waterflooding was conducted for 3 pore volumes injected of a fluid in a displacement experiment (e.g., coreflooding) (PVs) followed by another 3 PVs of biopolymer flooding. The prediction of the previously performed simulation runs (Al-Shalabi, 2018) in the tertiary mode of injection was about 2% incremental OOIP at 6 PVs of injection, which is equivalent to about 4% additional OOIP at 6 PVs. In order to check this discrepancy in additional oil by tertiary biopolymer injection, a validation study is conducted in this subsection.

Sensitivity Analysis. In the validation study, sensitivity analysis was mainly performed on each input parameter that was not reported in both Quadri (2015) and Li (2015) experimental works and was assumed in the previously performed base simulation runs. Also, other reported input parameters were considered to understand their effect on incremental oil recovery by biopolymer injection in the tertiary mode. These input parameters include inaccessible pore volume (IPV), adsorption, permeability reduction, shear rate coefficient, and hardness of the makeup water. These parameters as well as their different values are summarized in Table 1. Each of these parameters are discussed below in details. It is worth mentioning that the polymer concentration used in this valuation study is 200 ppm, which is in match with the experimental coreflood conducted by Li (2015).

TABLE 1 A summary of the parameters used in sensitivity analysis of tertiary polymer flooding using the UTCHEM simulator UTCHEM Variable Parameter Assigned Values Inaccessible Pore EPHI4 0.7, 0.8, 0.9, 1* Volume (IPV) Polymer Adsorption a_(p1) 0, 1.857*, 5.38, 53.8 Permeability Reduction c_(kr) 0, 0.00883*, 0.011, 0.013 Equivalent Shear Rate {dot over (γ)}_(c) 3.97, 10.12*, 19.85, 39.7 Hardness of Makeup Water β_(p) 0*, 1, 10, 20 *refers to the value used in the base simulation run.

Inaccessible Pore Volumes (IPV). The IPV was assumed as zero in the base simulation run. This was possible by assigning an effective porosity value (EPHI4) of 1 in the UTCHEM simulator where IPV=1−EPHI4. A sensitivity analysis was performed on IPV through adjusting the EPHI4 parameter in UTCHEM according to Table 2. The values selected for IPV are 0.1, 0.2, and 0.3.

TABLE 2 Sensitivity Analysis on inaccessible pore volume (IPV) Inaccessible Pore Effective Additional Oil Absolute Volume Porosity Recovery Difference (IPV) (EPHI4) (% OOIP) (% OOIP) 0   1   3.90 — (Base Case) 0.1 0.9 3.90 0.00 0.2 0.8 3.90 0.00 0.3 0.7 3.88 0.02

The effect of IPV on tertiary oil recovery by polymer flooding is depicted in Table 2 and FIG. 6, where cumulative oil recovery is shown on the y-axis and cumulative injection is shown on the x-axis. The results show that tertiary oil recovery by polymer flooding is insensitive to the IPV for the values selected. This is supported by the absolute difference calculations in Table 2, which compare each of the selected values to the base case value. In addition, this is supported from FIG. 6 where curves 602, 604, 606, and 608 at different values of IPV are overlapping. It should be noted that the selected values for IPV are typically reported in the literature for different polymer flooding experiments.

Polymer Adsorption. The polymer adsorption is captured in UTCHEM through the Langmuir-type isotherm where a_(p1) parameter is adjusted to capture adsorbed polymer concentration (Ĉ_(p)). In the base case, a_(p1) value of 1.857 was used to capture experimentally observed polymer adsorption of 6.9 μg/g of rock. A sensitivity analysis on polymer adsorption was performed through adjusting the a_(p1) parameter in UTCHEM according to Table 3. The values selected for polymer adsorption include 0, 20, and 200 μg/g of rock.

TABLE 3 Sensitivity Analysis on polymer adsorption Polymer Adsorption Additional Oil Absolute Adsorption Parameter Recovery Difference (μg/g of rock) (a_(p1)) (% OOIP) (% OOIP)   6.9  1.857 3.90 — (Base Case)   0    0    3.93 0.03  20    5.38  3.60 0.30 200   53.8   2.57 1.33

Both Table 3 and FIG. 7 show that polymer adsorption has a slight negative effect on oil recovery by polymer flooding. The increase in polymer adsorption leads to a decrease in the additional oil recovery obtained by tertiary polymer flooding. This is reasonable as the adsorbed amount of polymer will be lost from the aqueous phase and will not contribute to the viscosifying power of the polymer used. However, this effect is not well pronounced as seen in Table 3, where a one order of magnitude increase in adsorption (20 μg/g of rock) results in a 0.3% absolute different in additional OOIP. Also, a two orders of magnitude increase in adsorption (200 μg/g of rock) results in 1.33% absolute difference in additional OOIP. The latter is also supported by FIG. 4, which reveals that the pink curve of 6.9 μg/g of rock is almost overlapping with that of 20 μg/g of rock (green curve). This finding holds for the range of the selected values for polymer adsorption, which is based on best scenario with no adsorption (0 μg/g of rock), worst scenario of very high adsorption levels (200 μg/g of rock) as well as typical values from the literature. It is worth mentioning that if such a high adsorption value of 200 μg/g of rock was obtained in the lab, then this polymer needs to be screened out as this adsorption indicates an unsuccessful as well as an uneconomical polymer flooding at field-scale.

Permeability Reduction. The reduction in effective water permeability (F_(kr)) because of polymer flooding is modeled in UTCHEM through adjusting the parameter (c_(kr)). For the base case, a c_(kr) value of 0.00883 was used to capture an experimentally observed permeability reduction of 3.9. The effect of permeability reduction factor (F_(kr)) on tertiary oil recovery was investigated through tuning the c_(kr) parameter in UTCHEM according to Table 4. The values selected for permeability reduction factor include 1, 6, and 10.

TABLE 4 Sensitivity Analysis on permeability reduction by polymer flooding Permeability Permeability Additional Oil Absolute Reduction Reduction Parameter Recovery Difference (F_(kr)) (c_(kr)) (% OOIP) (% OOIP)  3.9 0.00883 3.90 — (Base Case)  1   0      3.00 0.90  6   0.011   4.68 0.78 10   0.013   5.00 1.1 

The effect of permeability reduction factor on oil recovery by polymer flooding is depicted in Table 4 and FIG. 8. The results show that with increasing the permeability reduction factor, the additional oil recovery by polymer flooding increases. This effect is reasonable as with increasing the permeability reduction factor, water effective permeability decreases, which decreases the water cut and promotes more oil production. The analysis also shows that there is a pronounced difference between the case of no permeability reduction (F_(kr) of zero) compared to the other cases with different F_(kr) values (Table 4). FIG. 8 supports the latter where there is a clear difference between the curve of zero permeability reduction and the other curves, as shown in graph 800. The permeability reduction effect holds for the results chosen for this study. The experimentally reported value of 3.9 sounds reasonable and the other values were utilized to study the effect of this parameter. Nevertheless, one should note that higher values up to 10 are unlikely to occur.

Equivalent Shear Rate. The UTCHEM simulator captures the effect of shear rate on polymer viscosity through considering the equivalent shear rate ({dot over (γ)}_(eq)), which is defined using Cannella equation. In this equation, the equivalent shear rate is a function of {dot over (γ)}_(c) parameter where the latter depends on shear rate coefficient (C) as {dot over (γ)}_(c)=3.97 C. The shear rate coefficient was assumed in the base simulation run as 2.55 based on the work conducted by Kulawardana, E. U., Koh, H., Kim, D. H., Liyanage, P. J., Upamali, K., Huh, C., Weerasooriya, U., and Pope, G. A., 2012. Rheology and Transport of Improved EOR Polymers under Harsh Reservoir Conditions. Paper SPE 154294, SPE Improved Oil Recovery Symposium, Tulsa, Okla., USA, hereinafter, “Kulawardana et al. (2012)”. Hence, sensitivity analysis was performed on this parameter through tuning the γ_(c) parameter in UTCHEM according to Table 5. Different values were considered for shear rate coefficient including 0, 1, 5, and 10.

TABLE 5 Sensitivity Analysis on shear rate coefficient Shear Rate Effective Shear Additional Oil Absolute Coefficient Rate Parameter Recovery Difference (C) ({dot over (γ)}_(c)) (% OOIP) (% OOIP)  2.55 10.12 3.90 — (Base Case)  0    0.00 7.96 4.06  1    3.97 4.56 0.66  5   19.85 3.89 0.01 10   39.70 3.87 0.03

The effect of shear rate coefficient on tertiary oil recovery by polymer flooding is depicted in Table 5 and FIG. 9. The results show insensitivity of polymer flooding to shear rate effect; meaning that as shear rate coefficient increases above 1, oil recovery is not much affected. This is supported from Table 5 through the negligible absolute different in (%) OOIP as well as FIG. 9 through the overlapping curves 900. Waterflooding was simulated up to 6 PVs to check if there is still an effect of polymer on oil recovery when using high shear rate coefficient values. The results show that although the high values of shear rate coefficients used, oil recovery by polymer flooding is still favorable compared to continuous water injection up to 6 PVs.

Another interesting observation is that at zero shear rate coefficient, which means when neglecting the shear rate effect, oil recovery by polymer was the highest as expected and a fair history match was obtained for the oil recovery data. Nevertheless, the last scenario is not reasonable and neither realistic as effective shear rate has to occur due to the polymer molecules slippage effect within the porous media and both porosity and permeability contributes to this effect especially in formations with relatively high heterogeneity.

Hardness of Makeup Water. The effect of makeup water hardness on tertiary oil recovery by polymer flooding was investigated. Water salinity and harness effects are modeled in UTCHEM through the effective polymer salinity parameter (C_(sep)). The water hardness in specific is captured through the β_(p) parameter, which was not measured in the lab and has a typical value of 10 from the literature. In the base simulation run, the effect of makeup water hardness was neglected through considering β_(p) with a value of 1. Hence, sensitivity analysis was performed to study the significance of water hardness through adjusting the β_(p) parameter in UTCHEM according to Table 6. Different values were considered for water hardness including 10, 20, and 40. These assigned values are typical for makeup waters used for synthetic- and bio-polymers.

TABLE 6 Sensitivity Analysis on makeup water hardness Hardness Additional Oil Absolute Parameter Recovery Difference (β_(p)) (% OOIP) (% OOIP)  1 3.90 — (Base Case) 10 3.89 0.01 20 3.80 0.1  40 3.74 0.16

Table 6 and FIG. 10 show that there is a slight decrease in oil recovery with increasing the water hardness as expected. However, this effect is not well pronounced. The latter is supported by the negligible absolute different in (%) OOIP (Table 6) and the almost overlapping curves 1000 in FIG. 10. It should be noted that in this analysis, the overall water salinity was kept constant and only the hardness factor was adjusted.

As seen from the above analysis, the sensitivity analysis performed for different assumed or not reported input parameters was not able to history match the oil recovery data. Neither the analysis was able to provide an insight on the controlling factor underlying the additional oil recovery caused by tertiary polymer flooding. Trapping number effect is discussed in the next subsection as a trial to understand this additional oil recovery by polymer flooding in carbonates.

Trapping Number. In this work, the trapping number was calculated twice; for the waterflooding period of 3 PVs, and the subsequent polymer flooding period for an additional 3 PVs. N_(Tl) calculations are listed in Table 7.

TABLE 7 Trapping number calculations for waterflooding and polymer flooding cycles Darcy Aqueous phase Trapping Injection Injection Velocity Viscosity @ IFT Number Mode Cycle (ft/day) 120° C. (cP) (dynes/cm) (N_(T)) S_(or) Secondary Waterflooding 0.833 0.385 30 3.77 × 10⁻⁸ 0.251 Tertiary Polymer 0.833 10 30 9.80 × 10⁻⁷ 0.1 Flooding

An interesting finding from this table is that the trapping number was increased by about two orders of magnitude during polymer flooding compared to that during waterflooding. This increase in trapping number is mainly due to the increase in the aqueous phase viscosity by introducing polymer to the solution. There is a high possibility that this increase in residual oil saturation has led to a decrease in residual oil saturation especially for carbonates. Hence, the relation between trapping number and residual oil saturation was investigated.

This relation has been measured and practiced by different researchers in the literature for carbonate rocks similar to the ones used by Li (2015) (Kamath, J., Rober, F. M., and Frank, M. N., 2001. Understanding Waterflood Residual Oil Saturation of Four Carbonate Rock Types. Paper SPE 71505, SPE Annual Technical Conference and Exhibition, New Orleans, La., USA, hereinafter, “Kamath et al., (2001)”; Abrams, A., 1975. The Influence of Fluid Viscosity, Interfacial Tension, and Flow Velocity on Residual Oil Saturation Left by Waterflood. SPE Journal, 15(5): 437-447, hereinafter, “Abrams, 1975”; Al-Shalabi, E. W., Sepehrnoori, K., Pope, G., and Mohanty, K., 2014. A Fundamental Model for Prediction Oil Recovery due to Low Salinity Water Injection in Carbonate Rocks. Paper SPE 169911, SPE Trinidad & Tobago Energy Resources Conference, Port of Spain, Trinidad and Tobago, hereinafter, “Al-Shalabi et al., 2014”). The carbonate cores used by Li (2015) are similar to sample K3 in the work reported by Kamath et al. (2001). This is evident from the trapping number vs. residual oil saturation data 1100 shown in FIG. 11. In FIG. 11, at the applied trapping number during waterflooding (3.77×10⁻⁸), the residual oil saturation (S_(orw)) has a value which is similar to the one reported in the lab of 0.251. Interestingly, at the applied trapping number during polymer flooding (9.80×10⁻⁷), the residual oil saturation (S_(orp))) decreases to about 0.1 (Table 7). Therefore, the increase in oil recovery during tertiary polymer flooding is related to the increase in trapping number and this relation needs to be captured in history matching the data.

The capillary desaturation curve (CDC) model was applied in this work, where S_(lr) ^(high) is assumed zero as usual, S_(ir) ^(low) is 0.251 which is the residual oil saturation value obtained during waterflooding cycle, τ is assumed as 0.8 which is a typical value in the literature for carbonates, and T_(l) is a matching parameter with a value of 100,000. This latter parameter was obtained through tuning the relation to capture the residual oil saturation (S_(orp)) during the application of high trapping number during polymer flooding cycle.

The modeled CDC relation as well as the calculations made are depicted in Table 8 and FIG. 12. It is worth mentioning that the relation was captured for both sandstone and carbonate rocks to highlight the difference. Usually, for sandstone rocks, the i parameter has a value of 1 and the trapping parameter (T_(i)) is between 20,000 to 30,000. FIG. 12 shows that at the applied trapping number during polymer flooding (9.80×10⁻⁷), the critical trapping number (N_(T)*) of sandstones has not been exceeded. Usually, N_(T)* for sandstones are within 10⁻⁶ order of magnitude. On the other hand, the N_(T)* for carbonates has been exceeded which it is at least one to two orders of magnitude lower than that of sandstones. Usually, carbonates have a shallower CDC curve compared to that of sandstones, due to the relatively high heterogeneity of carbonates. Hence, it is easy to extract some of the oil from carbonates, but difficult to extract the rest. Whereas in sandstones, as soon as the critical trapping number is exceeded, most of the oil is produced.

TABLE 8 CDC calculations for sandstone and carbonate rocks Carbonate Rock Sandstone Rock S_(or) (high) 0.000 S_(or) (high) 0.000 S_(or) (low) 0.251 S_(or) (low) 0.251 T₁ 100,000 T₁ 25,000 τ 0.8 τ 1 N_(T) Calculated S_(or) N_(T) Calculated S_(or) 1.00 × 10⁻¹⁰ 0.251 1.00 × 10⁻¹⁰ 0.251 1.60 × 10⁻⁹  0.249 1.60 × 10⁻⁹  0.251 2.56 × 10⁻⁸  0.231 2.56 × 10⁻⁸  0.251 8.19 × 10⁻⁷  0.107 8.19 × 10⁻⁷  0.246 1.64 × 10⁻⁶  0.075 1.64 × 10⁻⁶  0.241 5.24 × 10⁻⁵  0.006 5.24 × 10⁻⁵  0.109 1.05 × 10⁻⁴  0.004 1.05 × 10⁻⁴  0.069 6.71 × 10⁻³  0.000 6.71 × 10⁻³  0.001 5.37 × 10⁻²  0.000 5.37 × 10⁻²  0.000 1.35 × 10⁻¹  0.000 1.35 × 10⁻¹  0.000

The trapping number effect on relative permeability curves was considered as well. Table 9 summarizes the calculated relative permeability parameters before and after exceeding the critical trapping number. Also, FIG. 13 shows the relative permeability curves before and after exceeding the critical trapping number. It should be noted that for the water phase, k_(rw)*^(high), was k_(rl) ^(o) ^(high) assumed to be 0.3 which is a reasonable value because of the initially low endpoint water relative permeability (k_(rw)*^(low)) during waterflooding of 0.063 and n_(w) ^(high) was assumed to be 1. Also, one should note that for the oil phase, endpoint relative permeability and Corey's exponent remained constant after exceeding the critical trapping number. This is because of the assumed constant irreducible water saturation.

TABLE 9 Relative permeability parameters before and after exceeding N_(T)* Injection Mode Secondary Tertiary Injection Cycle Waterflooding Polymer Flooding Applied N_(T) Below N_(T)* Exceeding N_(T)* Relative n_(w) 1.5 1.2 Permeability n_(o) 1.5 1.5 Parameters k_(rw)* 0.063 0.206 k_(ro)* 0.104 0.104 S_(or) 0.251 0.1 S_(wirr) 0.304 0.304

The adjusted relative permeability curves as well as residual oil saturation using the CDC model at high trapping number were incorporated in history matching of tertiary oil recovery by the Schizophyllan biopolymer. The results are depicted in FIG. 14, which shows a reasonable history match of Li (2015) data after considering the trapping number effect. Table 10 shows that the additional oil recovery obtained using this history matching approach is 8.85%, which is within the range reported by Li (2015) for polymer flooding post waterflooding (7-10% OOIP). FIG. 15 shows the successfully history matched coreflooding of the Schizophyllan biopolymer including both waterflooding and polymer flooding cycles.

TABLE 10 Trapping number effect on oil recovery by polymer flooding Additional Oil Absolute Recovery Difference Trapping Number (N_(T)) Condition (% OOIP) (% OOIP) Without N_(T) Effect (Base Case) 3.90 — With N_(T) Effect 8.85 4.95

The previous analysis shows that by including trapping number effect, residual oil saturation was reduced to 10% as opposed to 20% without considering its effect. The pronounced effect of trapping number in this case is due to the increase in water viscosity post-polymer flooding compared to pre-polymer flooding, about two orders of magnitude increase. The common practice of neglecting trapping number effect during polymer flooding might be misleading. Trapping number effect should be treated as case dependent. The study at the laboratory-scale is considered as a basis for field-scale predictions.

Polymer Properties Modeling

In this section, modeling of the different properties of polymer flooding using the UTCHEM simulator is discussed.

Polymer Viscosity, Salinity, and Concentration. Polymer viscosity is important in mobility control of the injected polymer solution. Polymer viscosity increases with increasing polymer concentration whereas it decreases with increasing the solution salinity. The dependence of polymer solution viscosity at zero shear rate (μ_(p) ⁰) on both polymer concentration and salinity are modeled in UTCHEM using the Flory-Huggins equation as follows (Flory, P. J., 1953. Principles of Polymer Chemistry. Cornell University Press, hereinafter, “Flory, 1953”):

μ_(p) ⁰=μ_(w)(1+(A _(p1) C _(p) +A _(p2) C _(p) ² +A _(p3) C _(p) ³)C _(sep) ^(S) ^(p) ),  (1)

where μ_(w) is the water viscosity in cP, C_(p) is the polymer concentration in water, A_(p1), A_(p2), A_(p3), and S_(p) are fitting constants, and C_(sep) is the effective polymer salinity. It should be noted that the units for the parameters inside the parentheses must be dimensionless so that the unit for μ_(p) ⁰ be the same as μ_(w). C_(sep) captures the dependency of polymer viscosity on both salinity and hardness, and is defined as:

$\begin{matrix} {{C_{sep} = \frac{C_{51} + {\left( {\beta_{p} - 1} \right)C_{61}}}{C_{11}}},} & (2) \end{matrix}$

where C₅₁ and C₆₁ are the anion and the divalent concentration in the aqueous solution in meq/mL, respectively. C₁₁ is the water concentrations in the aqueous phase and it is expressed as water volume fraction in the aqueous phase. β_(p) is measured in the laboratory, with typical value of about 10. In C_(sep) calculation, usually the total amount of chloride ion is considered because NaCl is the most common salt in the water used and the current technology cannot describe the effect of every single ion on chemical EOR. It is worth mentioning that S_(p) is the slope of

$\frac{\mu_{p}^{0} - \mu_{w}}{\mu_{w}}$

versus C_(sep) on a log-log plot.

Shear Effect. Biopolymer solutions are consider pseudoplastic or shear thinning fluids, which means that their viscosity decreases with increasing the shear rate. In UTCHEM, the shear effect on polymer viscosity is modeled using Meter's equation, which is defined as (Meter, D. M. and Bird, R. B., 1964. Tube Flow of Non-Newtonian Polymer Solutions: Part I Laminar Flow and Rheological Models. AlChE Journal, 10(6):878-881, hereinafter, “Meter and Bird, 1964”):

$\begin{matrix} {{\mu_{p} = {\mu_{w} + \frac{\mu_{p}^{0} - \mu_{w}}{1 + \left( \frac{{\overset{.}{\gamma}}_{eq}}{{\overset{.}{\gamma}}_{1/2}} \right)^{({P_{\alpha} - 1})}}}},} & (3) \end{matrix}$

where P_(α) is an empirical parameter that is obtained by matching laboratory-measured viscosity data, μ_(p) ⁰ is the limiting viscosity at low shear limit (approaching zero), μ_(w) is the water viscosity which is the limiting viscosity at high shear limit (approaching infinity), and {dot over (γ)}_(1/2) is the shear rate at which polymer viscosity is the average of the μ_(p) ⁰ and μ_(w). The equivalent shear rate ({dot over (γ)}_(eq)) is defined using Cannella equation as follows (Cannella, W. J., Huh, C., and Seright, R. S., 1988. Prediction of Xanthan Rheology in Porous Media. Paper SPE 18089, SPE Annual Technical Conference and Exhibition, Houston, Tex., USA, hereinafter, “Cannella et al., 1988”):

$\begin{matrix} {{{\overset{.}{\gamma}}_{eq} = \frac{{\overset{.}{\gamma}}_{c}{❘u_{l}❘}}{\sqrt{\overset{\_}{k}k_{rl}\phi S_{l}}}},} & (4) \end{matrix}$ $\begin{matrix} {{{\overset{.}{\gamma}}_{c} = {{3.9}7C}},} & (5) \end{matrix}$

where u is Darcy's velocity in ft/day, k is the formation average permeability in Darcy, and C is a constant that depends on permeability and porosity.

Polymer Adsorption. Polymer retention could be either dynamic (mechanical trapping and hydrodynamic trapping) or static (adsorption). Mechanical trapping occurs due to the use of polymers with sizes greater than the pores of the porous medium and it happens during polymer flow. The latter could be controlled by using polymers in high permeability medium or pre-shearing of polymer solution. Hydrodynamic trapping occurs also during polymer flow in the medium where the polymer retention depends on the flow rate. Usually, this effect is negligible especially at field-applications. Adsorption is the most important mechanism, which occurs due to the interaction between polymer molecules and the solid surface. Adsorption depends on the surface area exposed to the polymer solution. Researchers usually use the term polymer retention to describe polymer loss or they simply use the term adsorption (Sheng, J. J., 2011. Modern Chemical Enhanced Oil Recovery-Theory and Practice. Gulf Publishing, Elsevier, hereinafter, “Sheng, 2011”).

In UTCHEM, the Langmuir-type isotherm is used to describe polymer adsorption as follows (Lakatos, I., Lakatos-Szabo, J., and Toth, J., 1979. Factors Influencing Polyacrylamide Adsorption in Porous Media and their Effect on Flow Behavior. 3^(rd) International Conference on Surface and Colloid Science Symposium, Stockholm, hereinafter, “Lakatos et al., 1979”):

$\begin{matrix} {{{\overset{\hat{}}{C}}_{p} = {\min\left( {C_{p},\frac{a_{p}\left( {C_{p} - {\overset{\hat{}}{C}}_{p}} \right)}{1 + {b_{p}\left( {C_{p} - {\overset{\hat{}}{C}}_{p}} \right)}}} \right)}},} & (6) \end{matrix}$

where C_(p) is the injected polymer concentration, Ĉ_(p) is the adsorbed polymer concentration, C_(p)−Ĉ_(p) is the equilibrium concentration in the rock-polymer solution system, a_(p) and b_(p) are empirical constants. It should be noted that both C_(p) and Ĉ_(p) have the same units, and b_(p) has the reciprocal unit of C_(p). Also, a_(p) is dimensionless and defined as:

$\begin{matrix} {{a_{p} = {\left( {a_{p1} + {a_{p2}C_{sep}}} \right)\left( \frac{k_{ref}}{k} \right)^{0.5}}},} & (7) \end{matrix}$

where a_(p1) and a_(p2) are fitting parameters, C_(sep) is the effective salinity, k is the formation permeability, and kref is the reference permeability of the rock used in the laboratory measurement for adsorption. It must be noted that Langmuir model assumes equilibrium conditions, instantaneous polymer adsorption as well as reversible adsorption in terms of polymer concentration. Polymer adsorption depends on polymer type, salinity, and rock surface.

Permeability Reduction. There is a noticeable formation permeability change during polymer flooding compared to waterflooding. This permeability reduction is due to polymer adsorption. The permeability reduction factor (F_(kr)) is defined as:

$\begin{matrix} {{F_{kr} = \frac{k_{{eff},w}}{k_{{eff},p}}},} & (8) \end{matrix}$

where k_(eff,w) is the rock effective permeability when rock is flooded by water and k_(eff,p) is the rock effective permeability when the rock is flooded with polymer solution. This factor is modeled in UTCHEM using the following equations:

$\begin{matrix} {{F_{kr} = {1 + {\left( {F_{{kr},\max} - 1} \right)\left( \frac{b_{kr}C_{p}}{1 + {b_{kr}C_{p}}} \right)}}},} & (9) \end{matrix}$ $\begin{matrix} {{F_{{kr},\max} = {\min\left\{ {\left( {1 - \frac{{c_{kr}\left( {A_{p1}C_{sep}^{S_{p}}} \right)}^{1/3}}{\sqrt{\frac{k}{\phi}}}} \right)^{- 4},\ 10} \right\}}},} & (10) \end{matrix}$

where b_(kr) and c_(kr) are input parameters derived from data matching, A_(p1) is the constant in Equation (1) and C_(sep) is calculated using Equation (2). It should be noted that the term b_(kr)C_(p) must be dimensionless, similarly is the case for F_(kr,max), which has an assumed empirical value of 10.

As the polymer adsorption process can be considered sometimes irreversible due to the prolonged pore volumes of water injection to restore the initial permeability, the residual resistance factor (F_(rr)) was introduced. The latter parameter is defined as the ratio of water mobility before polymer flow to water mobility after polymer flow. However, F_(rr) does not take into account the increase in viscosity caused by polymer flooding. Hence, the resistance factor term (F_(r)) was introduced, which is defined as the ratio of water mobility during water flow to polymer mobility during polymer flow. It should be noted that in UTCHEM, viscosity increase and permeability reduction due to polymer flooding is only applicable to the water phase by modifying the polymer viscosity by F_(kr).

Inaccessible Pore Volume (IPV). It refers to the fraction of pore volume where the radii of the pores are smaller than the size of polymer particles, especially when polymers with high molecular weight are used. These pores are usually filled with irreducible or connate water. IPV has a positive effect on sweep efficiency of polymer solutions and hence, better oil recovery due to boosting the advancement of the polymer solution front. Moreover, the IPV is useful from an economical point of view where it results in less contact between rock surface and polymer solution and hence, less polymer adsorption/retention. The only disadvantage of IPV is when these inaccessible pores have movable oil droplets. In this situation, polymer solutions will not be able to contact these oil droplets and that oil remains as residual oil saturation (Dawson, R. and Lantz, R. B., 1971. Inaccessible Pore Volume in Polymer Flooding. Paper SPE 3522, SPE Annual Fall Meeting, New Orleans, La., USA, hereinafter, “Dawson and Lantz, 1971”). IPV is modeled using UTCHEM by multiplying the porosity in the conservation equation for polymer by an input parameter (EPHI4) defined as the effective porosity. EPHI4 is 1−IPV.

Trapping Number

The trapping number concept is usually not used in polymer flooding modeling due to the belief that the increase in aqueous viscosity by polymer does not cause further reduction in residual oil saturation. This observation is well observed for sandstones; however, as explained in this work that under certain conditions in carbonates the same concept is applicable. There are different definitions for the trapping number (N_(Tl)), but the most acceptable definition was introduced by Jin, M., 1995. A Study of Nonaqueous Phase Liquid Characterization and Surfactant Remediation. PhD Dissertation, The University of Texas at Austin, Tex., USA, hereinafter, “Jin (1995)” and is given by:

$\begin{matrix} {N_{Tl} = {\frac{\left| {\overset{\rightarrow}{\overset{\rightarrow}{k}}.\left\lbrack {{\nabla\Phi_{l^{\prime}}} + {{g\left( {\rho_{l^{\prime}} - \rho_{l}} \right)}{\nabla D}}} \right\rbrack} \right|}{\sigma_{{ll}^{\prime}}}.}} & (11) \end{matrix}$

Trapping number in Equation (11) can be expressed as a function of both capillary number and bond number. Capillary number (N_(cl)) is defined as the ratio of viscous forces to capillary forces. Bond number (N_(Bl)) is defined as the ratio of gravity forces to capillary forces. Hence, trapping number can also be expressed as follows:

$\begin{matrix} {{N_{Tl} = \sqrt{N_{cl}^{2} + {2N_{cl}N_{Bl}\sin\theta} + N_{Bl}^{2}}},} & (12) \end{matrix}$ $\begin{matrix} {{N_{cl} = \frac{\left| {\overset{\rightarrow}{\overset{\rightarrow}{k}}.{\nabla\Phi_{l^{\prime}}}} \right.❘}{\sigma_{{ll}^{\prime}}\cos\theta}},} & (13) \end{matrix}$ $\begin{matrix} {{N_{Bl} = \frac{{kg}\left( {\rho_{l^{\prime}} - \rho_{l}} \right)}{\sigma_{{ll}^{\prime}}\cos\theta}},} & (14) \end{matrix}$ $\begin{matrix} {{{\nabla\Phi_{l}^{\prime}} = {{\nabla P_{l^{\prime}}} - {g\rho_{l^{\prime}}{\nabla D}}}},} & (15) \end{matrix}$

where l′ is the displacing phase (aqueous phase including polymer), l is the displaced phase (oil phase), ∇Φ_(l′) is the flow potential gradient of the displacing phase, k is the permeability, g is the gravitational force constant, 0 is the angle measured from the horizontal level in Equation (12) and the contact angle in Equations (13) and (14), and σ_(ll′) is the interfacial tension between the displacing and displaced phases.

In the case of Li (2015), the corefloods were conducted horizontally, which makes θ in Equation (12) goes to zero. Therefore, the trapping number equation becomes as follows:

N _(Tl)=√{square root over (N _(cl) ² +N _(Bl) ²)}.  (16)

Further reduction can be introduced by neglecting the gravity contribution for the same good reason mentioned above, which leads to:

$\begin{matrix} {{N_{Tl} = {N_{cl} = \frac{v\mu}{\sigma_{ow}}}},} & (17) \end{matrix}$

where ν is Darcy velocity in the core, μ is the aqueous phase viscosity, and σ_(ow) is the interfacial tension between oil and water.

Delshad, M., 1990. Trapping of Micellar Fluids in Berea Sandstone. PhD Dissertation, The University of Texas at Austin, Tex., USA, hereinafter, “Delshad (1990)” introduced the dependence of S_(or) on the trapping number through the capillary desaturation curve (CDC) relation as follows:

$\begin{matrix} {{S_{lr} = {S_{lr}^{high} + \frac{S_{lr}^{low} - S_{lr}^{high}}{1 + {T_{l}N_{T_{l}}^{\tau}}}}},{{{for}l} = 1},\ldots,{np},} & (18) \end{matrix}$

where l is the phase number, T_(l) is phase trapping parameter, S_(lr) ^(low) S_(lr) ^(low) and S_(lr) ^(high) S_(lr) ^(high) are the residual phase saturations at low and high trapping numbers, respectively. τ is a parameter which depends on the pore size distribution of the rock.

Both relative permeability endpoints (k_(rl)*) and exponents (n_(l)) were also adjusted as a function of trapping number according to the Delshad model (Delshad, M., Bhuyan, D., Pope, G. A., and Lake, L., 1986. Effect of Capillary Number on the Residual Saturation of a Three-Phase Micellar Solution. Paper SPE 14911, SPE Enhanced Oil Recovery Symposium, Tulsa, Okla., USA, hereinafter, “Delshad et al. (1986)”), which is given by:

$\begin{matrix} {{k_{rl}^{*} = {{k_{rl}^{*^{low}} + {\frac{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}}{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}^{high}}\left( {k_{rl}^{*^{high}} - k_{rl}^{*^{low}}} \right)k_{rl}^{o}}} = {k_{rl}^{o^{low}} + {\frac{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}}{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}^{high}}\left( {k_{rl}^{{o}^{high}} - k_{rl}^{{o}^{low}}} \right)}}}},} & (19) \end{matrix}$ forl1, l^(′) = 1, …, np, $\begin{matrix} {{n_{l} = {{n_{l}^{low} + {\frac{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}}{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}^{high}}\left( {n_{l}^{high} - n_{l}^{low}} \right)n_{l}}} = {n_{l}^{low} + {\frac{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}}{S_{l^{\prime}r}^{low} - S_{l^{\prime}r}^{high}}\left( {n_{l}^{high} - n_{l}^{low}} \right)}}}},} & (20) \end{matrix}$ forl1, l^(′) = 1, …, np,

where the superscript high and low, corresponds to high and low trapping numbers, respectively.

Based on the disclosure and teachings provided herein, a person of ordinary skill in the art will appreciate other ways and/or methods to implement the various embodiments. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. It will, however, be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope of the disclosure as set forth in the claims.

Other variations are within the spirit of the present disclosure. Thus, while the disclosed techniques are susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the disclosure to the specific form or forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents falling within the spirit and scope of the disclosure, as defined in the appended claims.

The use of the terms “a” and “an” and “the” and similar referents in the context of describing the disclosed embodiments (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. The term “connected” is to be construed as partly or wholly contained within, attached to, or joined together, even if there is something intervening. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate embodiments of the disclosure and does not pose a limitation on the scope of the disclosure unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the disclosure.

Disjunctive language such as the phrase “at least one of X, Y, or Z,” unless specifically stated otherwise, is intended to be understood within the context as used in general to present that an item, term, etc., may be either X, Y, or Z, or any combination thereof (e.g., X, Y, and/or Z). Thus, such disjunctive language is not generally intended to, and should not, imply that certain embodiments require at least one of X, at least one of Y, or at least one of Z to each be present.

Preferred embodiments of this disclosure are described herein, including the best mode known to the inventors for carrying out the disclosure. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate and the inventors intend for the disclosure to be practiced otherwise than as specifically described herein. Accordingly, this disclosure includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the disclosure unless otherwise indicated herein or otherwise clearly contradicted by context.

All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein. 

1. A method of generating a prediction of an oil recovery from a reservoir induced by accomplishing an enhanced oil recovery technique that comprises injection of one or more fluids into the reservoir, the method comprising: simulating the reservoir in a computer simulation; simulating injection of a first fluid into the reservoir in the computer simulation; and simulating the oil recovery from the reservoir induced by accomplishing an enhanced oil recovery technique in the computer simulation so as to account for an estimated change in aqueous viscosity that would be induced by injection of the first fluid into the reservoir.
 2. The method of claim 1, wherein the computer simulation simulates: the reservoir in three dimensions; and multiphase flow within the reservoir.
 3. (canceled)
 4. The method of claim 2, further comprising simulating injection of a second fluid into the reservoir in the computer simulation, optionally wherein the first fluid is injected into the reservoir after the second fluid is injected into the reservoir in the enhanced oil recovery technique, or the first fluid comprises a polymer and the second fluid comprises water. 5.-6. (canceled)
 7. The method of any of claim 1, comprising: calculating a trapping number (N_(Tl)) for the reservoir that accounts for the first fluid within the reservoir, wherein the trapping number is defined as: $\frac{v\mu}{\sigma_{ow}}$ where ν is a Darcy velocity of a core sample comprising the same or similar material as the reservoir, μ is an aqueous phase viscosity, and σ_(ow) is an interfacial tension between oil and water.
 8. A method comprising: generating a model of a hydrocarbon reservoir having parameters; determining a critical trapping number for the hydrocarbon reservoir based in part on a substrate of the hydrocarbon reservoir; determining a trapping number of the substrate for a given injection volume; determining whether the trapping number has exceeded the critical trapping number; and modifying, based in part on the determination that the critical trapping number has been exceeded, one or more parameters of the model of the hydrocarbon reservoir.
 9. The method of claim 8, wherein generating the model of the hydrocarbon reservoir comprises generating the hydrocarbon reservoir in three dimensions and modeling multiphase flow within the hydrocarbon reservoir, optionally wherein the parameters of the hydrocarbon reservoir comprise residual oil and relative permeability, or wherein modifying the one or more parameters of the model comprises modifying the residual oil and relative permeability parameters. 10.-11. (canceled)
 12. The method of claim 8, wherein determining a trapping number of the substrate for a given injection volume comprises simulating injection of a first fluid into the model of the hydrocarbon reservoir, optionally wherein the first fluid comprises a polymer.
 13. (canceled)
 14. The method of claim 8, further comprising, determining expected oil recovery for a reservoir having a substrate that is the same as or similar to the substrate of the model of the hydrocarbon reservoir, optionally wherein determining the expected oil recovery comprises determining the expected oil recovery using an enhanced oil recovery technique.
 15. (canceled)
 16. A method of simulating oil recovery from a biopolymer injection cycle in a hydrocarbon carbonate reservoir, the method comprising: determining a critical trapping number representative of a simulated hydrocarbon carbonate reservoir based in part on a composition of a reservoir substrate; determining whether, for a given injection volume, a trapping number of a substrate of the hydrocarbon carbonate reservoir has exceeded a critical trapping number; and modifying residual oil and relative permeability parameters of the simulated hydrocarbon carbonate reservoir based on the determination that the critical trapping number has been exceeded.
 17. The method of claim 16, wherein, prior to determining the critical trapping number, the method further comprises simulating the hydrocarbon carbonate reservoir, optionally wherein the hydrocarbon carbonate reservoir is simulated in three dimensions and includes multiphase flow within the hydrocarbon carbonate reservoir.
 18. (canceled)
 19. The method of claim 16, wherein prior to determining whether the trapping number of the substrate has exceeded the critical trapping number, the method further comprises determining the trapping number of the substrate for the given injection volume, optionally wherein the trapping number (N_(Tl)) is defined as $\frac{v\mu}{\sigma_{ow}},$ where ν is a Darcy velocity of a core sample comprising the same or similar material as the hydrocarbon carbonate reservoir, μ is an aqueous phase viscosity, and σ_(ow) is an interfacial tension between oil and water.
 20. (canceled)
 21. The method of claim 19, wherein determining the trapping number comprises simulating injection of a first fluid into the simulated hydrocarbon carbonate reservoir, optionally wherein the first fluid comprises a polymer.
 22. (canceled)
 23. The method of claim 21, further comprising, determining expected oil recovery for a reservoir having a substrate that is the same as or similar to the substrate of the simulated hydrocarbon carbonate reservoir, optionally wherein determining the expected oil recovery comprises determining the expected oil recovery using an enhanced oil recovery technique.
 24. (canceled)
 25. A computer system comprising: rewritable memory; and a processor operable in response to execution instructions stored in the rewritable memory to: determine a critical trapping number representative of a simulated hydrocarbon reservoir based in part on a composition of a reservoir substrate; determine whether, for a given injection volume, a trapping number of the substrate has exceeded the critical trapping number; and modify residual oil and relative permeability parameters of the simulated hydrocarbon reservoir based on the determination that the critical trapping number has been exceeded.
 26. The computer system of claim 25, wherein, prior to determining the critical trapping number, the processor and rewritable memory are further operable to simulate the hydrocarbon reservoir, optionally wherein the hydrocarbon reservoir is simulated in three dimensions and includes multiphase flow within the hydrocarbon reservoir.
 27. (canceled)
 28. The computer system of claim 25, wherein prior to determining whether the trapping number of the substrate has exceeded the critical trapping number, the processor is further operable to determine the trapping number of the substrate for the given injection volume, optionally wherein the trapping number (N_(Tl)) is defined as $\frac{v\mu}{\sigma_{ow}},$ where ν is a Darcy velocity of a core sample comprising the same or similar material as the reservoir, μ is an aqueous phase viscosity, and σ_(ow) is an interfacial tension between oil and water.
 29. (canceled)
 30. The computer system of claim 25, wherein the processor and rewritable memory are further operable to, determine expected oil recovery for a reservoir having a substrate that is the same as or similar to the substrate of the simulated hydrocarbon reservoir, optionally wherein the expected oil recovery is determined for oil recovery using an enhanced oil recovery technique.
 31. (canceled) 